On Simple Formulations of Weakly-Singular Traction & Displacement BIE, and Their Solutions through Petrov-Galerkin Approaches

Using the directly derived non-hyper singular integral equations for displacement gradients [as in Okada, Rajiyah, and Atluri (1989a)], simple and straightforward derivations of weakly singular traction BIE’s for solids undergoing small deformations are presented. A large number of “intrinsic properties” of the fundamental solutions in elasticity are developed, and are used in rendering the tBIE and dBIE to be only weaklysingular, in a very simple manner. The solutions of the weakly singular tBIE and dBIE through either global Petrov-Galerkin type “boundary element methods”, or, alternatively, through the meshless local Petrov-Galerkin (MLPG) methods, are discussed. As special cases, the Galerkin type methods, which lead to symmetric systems of equations, are also discussed.